Debian – pgsql can connect, pgadmin cannot

https://www.postgresql.org/docs/current/static/auth-pg-hba-conf.html indicates that the order of entries maters, specifically:

Since the pg_hba.conf records are examined sequentially for each connection attempt, the order of the records is significant. Typically, earlier records will have tight connection match parameters and weaker authentication methods, while later records will have looser match parameters and stronger authentication methods. For example, one might wish to use trust authentication for local TCP/IP connections but require a password for remote TCP/IP connections. In this case a record specifying trust authentication for connections from 127.0.0.1 would appear before a record specifying password authentication for a wider range of allowed client IP addresses.

(so try reversing the order - put the line you are adding at the top)

Operating System User passwords (the thing you're asked for when you try to su) are not the same as Postgres User Passwords (the thing you don't need when you set auth to trust in pg_hba.conf).

You need to set a valid OS password for the Operating System's postgres user and enter that password in order to su to that user (Or su to that user from root, where you won't be asked for a password).

Typically the postgres OS user password is locked out after DB initialization since the only thing that needs to run as postgres is pg_ctl, which can be launched with su -c from your init scripts (that run as root and therefore don't need the password).